Chemical kinetics, order confusion

In the solution they've just directly used the first order equation (since overall order = 1) and got the answer. How did that work? Isn't the reaction half order with respect to A, so it should behave as such?
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Gamertug
Gamertug3w ago
order wrt A has no meaning , its just order
Gamertug
Gamertug3w ago
Order wrt A is like a Question
Nimboi [ping if answering]
ive seen that terminology used in questions it has to have some meaning
Gamertug
Gamertug3w ago
i meant it does not matter the overall order of reaction dictates the overall rate
Nimboi [ping if answering]
evidently not yeah but i dont conceptually get why
Gamertug
Gamertug3w ago
ic what u are trying to say
Nimboi [ping if answering]
my thought process was that if A is being consumed at a half order rate and so is B then to get details from A, we have to take its consumption behaviour into account
Gamertug
Gamertug3w ago
have u tried using that uh rate of formation = rate of being used
Nimboi [ping if answering]
hain? A aint being formed only being used
Gamertug
Gamertug3w ago
ye ik ,
Nimboi [ping if answering]
voh toh consecutive rxn mein hota hai na
Gamertug
Gamertug3w ago
wait tht wont work lemme try smth ngl it does feel counterintuivtive when we talk about A only
Nimboi [ping if answering]
yeh i tried dA/dt = K[A]^1/2 and then integration with initial and final concentration limits but i mean that just gave negative time and magnitude is also not the answer
727
7273w ago
what is the ans
SirLancelotDuLac
But dA/dt=k[A]^0.5 [B]^0.5 Which means [A] depends on [B] too In this case [A]=[B] Here dB/dt=dA/dt so, A=B+c From initial condition, c=0, so the rate of reaction depends on k[A]^0.5[B]^0.5=k[A] (since [A]=[B]) If you change the initial concentration ki condition, answer would be different.
Nimboi [ping if answering]
ahhh oke yeah that makes perfect sense gotcha, thank u 50sec @Gamertug explanation above ^ lmk if u understood, ill close it then
727
7273w ago
ok correct aya
Nimboi [ping if answering]
mast they're being consumed in an identical manner so its basically just equivalent to k[A] anyway so what if c wasnt equal to 0 suppose if B started out at 2 molar instead of 1
SirLancelotDuLac
Yeah but beware of situations where initial concentrations are not same. Then that would be done by differential rate law.
727
7273w ago
reference point hai i think
SirLancelotDuLac
Then dA/dt=ksqrt(A)sqrt(A+1) and then you solve to get dA/sqrt((A+1/2)^2-1/4)=kdt which gives you ln(A+sqrt(A^2+A)) with limits=k*t.
Nimboi [ping if answering]
that makes sense na actually wait arent there any number of functions between 2 numbers 1 to 2 is a simple example but there are prob other alternatives compared to A+1
SirLancelotDuLac
This point?
Nimboi [ping if answering]
yeah nvm got it
727
7273w ago
Ok but what if it’s not like just A+1 but more like to the point you ignore it
Gamertug
Gamertug3w ago
thx ahh ic
Nimboi [ping if answering]
+solved SirLancelotDuLac
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